Shape similarity measure for body tissue

ABSTRACT

A shape similarity metric can be provided that indicates how similar two or more shapes are. A difference between a union of the shapes and an intersection of the shapes can be used to determine the similarity metric. The shape similarity metric can provide an average distance between the shapes. Different processes for determining shapes can be evaluated for accuracy based on the shape similarity metric. New or alternative shape-determining processes can be compared for accuracy against other shape-determining processes including reference shape-determining processes. Shape similarity metrics can be determined for two-dimensional shapes and three-dimensional shapes.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.14/746,504 filed on Jun. 22, 2015 which claims priority and benefit fromU.S. Provisional Application No. 62/015,325, filed Jun. 20, 2014,entitled “A NEW SHAPE SIMILARITY MEASURE,” the entire contents of whichare incorporated herein by reference for all purposes.

TECHNICAL FIELD

The present disclosure generally relates to image processing, and moreparticularly to comparing shapes determined for body tissues in imagesof one or more patients, e.g., to improve shape-determining processesand to determine suitable treatment plans.

BACKGROUND

In image processing, there is a need for tools for an automated qualityassessment of different algorithms. Typically, there is interest in acomparison against a gold standard or against a previous version of analgorithm.

In the area of automated organ outlining on medical images like CT orMRI, there is the need for an efficient, robust and comprehensiblemethod of comparing different shapes. For example, algorithms can beused for determining a shape of an organ (e.g., kidney, liver, etc.). Itis desirable to assess a quality of the determined shape.

Existing methods for comparing shapes include the Dice similaritymeasurement and the Hausdorff distance measurement, but they can beinaccurate or at least provide undesirable results. For example, theDice similarity measurement is affected by the scale of the shapes witha fixed offset, indicating a better match as the shapes increase insize. Also, the metric produced by the Dice similarity measurement is aunitless ratio of similarity, which may be unhelpful for certain typesof comparisons. The Hausdorff distance measurement produces a metricwith distance units, but the Hausdorff distance measurement can providemisleading results because the process can be dramatically affected byoutlying points. Also, the measurement can be difficult to executeproperly.

Therefore, it is desirable to provide techniques for addressing theseproblems.

BRIEF SUMMARY

Embodiments of the present invention provide systems, methods, andapparatuses for assessing a quality of a determined shape in an image.For example, the quality can be determined by comparing twodifferently-determined shapes of a body tissue (e.g., organ or tumor)based on images of a patient. A first shape of the body tissue can bedetermined by a first shape-determining process (e.g. manual analysis byan expert), and first data can be received that defines a first boundaryof the first shape. Also, a second shape of the body tissue can bedetermined by a second shape-determining process (e.g. shape recognitionsoftware), and second data can be received that defines a secondboundary of the second shape. The shapes can then be compared to assessan accuracy of one of the shape-determining processes.

In one embodiment, an intersection of the two shapes and a union of thetwo shapes can be determined. A difference between the union and theintersection can be calculated, and a shape similarity metric can becomputed based on the difference. In this manner, a similarity metriccan be provided that determines that accuracy of the secondshape-determining process relative to the first shape-determiningprocess. To facilitate the comparison, the first shape and second shapecan both be placed in a same coordinate system (also called coordinatespace).

Other embodiments are directed to systems and computer readable mediaassociated with methods described herein.

A better understanding of the nature and advantages of embodiments ofthe present invention may be gained with reference to the followingdetailed description and the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows three examples of Dice coefficients for concentric circles.

FIG. 2 shows an example of a Hausdorff distance measurement.

FIG. 3 shows an approximation for calculating the difference between twoshapes according to embodiments of the present invention.

FIG. 4 is a flowchart illustrating a method for determining an accuracyof shape-determining processes for identifying shapes of a body tissuein one or more images of a patient according to embodiments of thepresent invention.

FIG. 5 shows an example where it is unclear which points arecorresponding between two shapes.

FIG. 6 shows two shapes with random curvature to illustrate a generaldifference formula according to embodiments of the present invention.

FIG. 7 is a flowchart illustrating a method for determining an accuracyof a shape-determining process, where there is no overlapping of shapesaccording to embodiments of the present invention.

FIG. 8 is a flowchart illustrating a method of comparing shapes of bodytissues in images of patients according to embodiments of the presentinvention.

FIG. 9 shows a block diagram of an example computer system usable withsystem and methods according to embodiments of the present invention.

DETAILED DESCRIPTION

Medical imaging (e.g. CT or MRI) can be used to evaluate the shapes ofcertain body tissues. However, the tissue of interest can be partiallyblocked by other body tissue, and the image can be otherwise unclear.Some applications (e.g. radiotherapy) depend on knowing the actual shapeof a tissue, so various methods have been developed for determining anactual tissue shape from an unclear medical image. For example, aradiologist may review one or more images and draw the outline of a bodytissue present in the images based on past experience. However, thereliance on manual evaluation is costly and inefficient. The descriptionincludes examples for organs, but is equally applicable to any bodytissue, including tumors.

Software algorithms exist for identifying shapes, but such algorithmsneed refinement. It can be difficult to assess an accuracy of a new orrefined algorithm. Accordingly, there is a need for assessing whether ashape-determination process is accurate. Embodiments can provide a newmetric that is invariant with size, and thus provide a more desirableway to assess a quality of a shape-determining process.

Accordingly, embodiments provide techniques for determining a similaritybetween two shapes, and thus allow assessing an accuracy of a processfor determining a shape. Embodiments can place the two shapes onto acommon coordinate space and determine an intersection area and unionarea created by the superimposed shapes. A shape similarity metric witheasily interpretable units (e.g. distance units) can be determined basedon a difference between the intersection and the union of the shapes.The shape similarity metric can indicate the accuracy of ashape-determining process. For example, a lesser difference between theunion and intersection can lead to a lesser shape similarity metric andindicate a higher accuracy of a shape-determining process.

In some embodiments, the average distance between the outlines(boundaries) of the intersection area and union area is determined as asimilarity metric. In one implementation, the distance between theintersection and the union can be directly measured at several pointsand then averaged. In another implementation, a distance metric can bedetermined based on the numerical values of the intersection area/volumeand union area/volume. A normalization factor can be determined based onthe compared shapes, e.g., so as to obtain a distance that is comparableacross different pairs of shapes. The shapes can be overlapping shapesor non-overlapping shapes, and a shape of the body tissue may not existfrom one shape-determining process. Further, embodiments can apply totwo-dimensional and three-dimensional shapes, and can be expanded toinclude higher dimensional shapes.

I. Introduction

With the increasing importance of automatic segmentation and automaticquality control in radiotherapy, there is the need for an efficient,robust and comprehensible method of comparing different organ contourshapes that are based on medical images (e.g. CT or MRI). There is aneed for an absolute shape comparison metric that can be easilyinterpreted, that is meaningful in a clinical context, and that isunaffected by size scaling. With such a measurement one can define atolerance value for automatic safety checking. The current standardmethods, Dice similarity and Hausdorff distance, are difficult tointerpret and are often not meaningful in a clinical context. The Dicesimilarity is sensitive to the size of the shapes whereas Hausdorff canbe dominated too strongly by individual outliers and localabnormalities.

A. Imaging

Several techniques can be used for obtaining images of various objects,e.g., diagnostic images for diagnostic purposes. For example, medicalimaging techniques include CT, Mill, ultrasound, PET, and SPECT(spontaneous positron emission computer tomography). These imagingtechniques can provide images of various body parts and biologicaltissues including glands, digestive organs (e.g., stomach or liver),bones, muscles, tendons, ligaments, cartilage, etc., collectivelyreferred to as organs. Organs can be of any body system, such asexcretory (e.g., kidneys), respiratory (e.g., lungs), etc. Typically, anorgan shape is determined by identifying the organ within an image, butan organ shape can also be determined by other processes (e.g. taking asurface scan of a spectrum reflected from an organ). Embodimentsdescribed herein for comparing shapes and determining accuracy ofshape-determining processes can be applied to any suitableshape-determination process. Further, the embodiments described hereincan be used for comparing any type of shape, including one-dimensionalshapes, two-dimensional shapes, three-dimensional shapes, andfour-dimensional shapes.

B. Comparison

When a shape of an organ is determined by a new shape determinationprocess, it is desirable to determine the accuracy of the shape, andthereby be able to evaluate the accuracy of the shape-determiningprocess. The accuracy of a shape (and shape-determining process) can bedetermined by comparing the shape with a reference shape (e.g., a goldstandard or other reliable shape-determining process). Accordingly, acontour comparison may be used for evaluating the quality of asegmentation algorithm, by comparing contours produced by the algorithmwith the reference shape.

For example, an organ (e.g. a spleen or pancreas) may be visible in a CTimage. Certain portions or boundaries of the organ may be blocked orunclear in the image. An expert radiologist may analyze the image anddetermine the shape and boundaries of the organ. Because an expert mayhave extensive experience and may be able to produce accurate andreliable shapes, the shape can be regarded as a reference shape.Alternatively, multiple experts (medical doctors, radiologists, etc.)may each draw or otherwise provide a version of the organ shape based onthe image, and the shapes can be averaged to determine the goldstandard. Such a reference shape can be used as a comparison/benchmarkfor evaluating the accuracy of shapes determined by other processes.

Besides image analysis by experts, there may be several other algorithmsand processes for determining the shape of an organ that is visible inan image. For example, a resident clinician (who may be learning to drawoutlines of organs based on images) can produce another version of theorgan. The resident's shape can be compared against the gold standard(e.g. a shape drawn by a supervising medical doctor). This can be aquality assurance process that critiques the resident-produced shape andhelps residents to improve their technique.

Automated computer-implemented algorithms may also be able to identifycontours and boundaries of an organ within an image.Computer-implemented algorithms may be significantly faster than manualimage analysis by an expert. Examples of alternative algorithms fordetermining an shape within an image are described in Dominique P.Huyskens et al., “A qualitative and a quantitative analysis of anauto-segmentation module for prostate,” Radiotherapy and Oncology 90(2009) 337-345, as well as in B. Hass et al., “Automatic segmentation ofthoracic and pelvic CT images for radiotherapy planning using implicitanatomic knowledge and organ-specific segmentation strategies,” Phys.Med. Biol. 53 (2008) 1751-1771. Computer-implemented algorithms couldeven be more reliable than a manually determined image.

In order to determine the accuracy of a new algorithm, an organ shapedetermined by the algorithm may be compared with a reference shape. Ifthe shapes are similar the algorithm can be deemed accurate, while ifthe shapes are dissimilar the algorithm may be considered inaccurate.Once the accuracy of the new algorithm is determined, it can be comparedwith past algorithms to see if it is better or worse than the pastalgorithms. Also, it can be decided whether or not to use the algorithmin real applications. The algorithm can be changed and improved, and thealgorithm can be continuously compared with a reference to measureimprovement.

The accuracy metric can further be used for quality assessment. Forexample, if any changes are made to the algorithm, or to software thatcontains the algorithm, embodiments can be used again to determine ashape (based on the same image or other raw data), and the shape can becompared with a reference (which could be an old version of thealgorithm). This way, the comparison and accuracy metric can be used tomake sure that the algorithm is performing the same as or better than itwas previously.

In some embodiments, a shape determined by applying an algorithm to animage can be compared with a shape determined by applying a previousversion of the same algorithm. An accuracy metric can be determined thatcan show whether or not the newer version of the algorithm is better,the same, or less accurate than the previous version. The new algorithmcould be faster and thus preferable, while providing a same level ofaccuracy. Thus, shapes determined by two different algorithms (neitherbeing a gold standard algorithm) can be compared.

C. Dice Similarity

One well-accepted method for comparing shapes is the Dice similaritymeasurement. The Dice similarity measurement is a simple measurementthat determines the overlapping percentage of two shape areas. Aunitless metric called the “Dice coefficient” is calculated. The formulaused is shown below:

${DICE} = \frac{2{{A_{1}\bigcap A_{2}}}}{{A_{1}} + {A_{2}}}$

The numerator multiplies the area of the intersection of the shapes bytwo, and the denominator is the sum of the areas of both shapes. Thenumerator is always equal to or smaller than the denominator, so theunitless Dice coefficient will be a number between zero and one.

An in-depth discuss of the Dice similarity measurement can be found inDice, Lee R. (1945), “Measures of the Amount of Ecologic AssociationBetween Species”, Ecology 26 (3): 297-302. DOI=10.2307/1932409, JSTOR1932409. A further discussion of segmentation techniques can be found inBabalola K O, Patenaude B, Aljabar P, Schnabel J, Kennedy D, Crum W,Smith S, Cootes T F, Jenkinson M, Rueckert D. (2008), “Comparison andevaluation of segmentation techniques for subcortical structures inbrain MRI”, Med Image Comput Assist Interv. 2008; 11(Pt 1):409-16.

FIG. 1 shows three examples of Dice coefficients for concentric circles.Circle 120 is compared against circle 125, and the dice coefficient isdetermined to be 0.85. Circle 140 is compared against circle 145, andthe dice coefficient is determined to be 0.72. Circle 160 is comparedagainst circle 165, and the dice coefficient is determined to be 0.62.As shown in FIG. 1, the distance between the inner circles (120, 140,160) and their respective outer circles (125, 145, 165) is the same.However, the dice coefficient is larger for the larger circles (120,125). This shows that the Dice coefficient is dependent on scale. Largershapes will tend to provide a higher Dice coefficient (indicating abetter match), even though, for two smaller shapes, the distance betweenthe inner shape and outer shape is the same.

In contrast to the Dice similarity measurement, embodiments can be scaleinvariant. For example, an average distance between two shapes canprovide a metric. The average distance between two shapes will alwaysresult in the same metric value, regardless of the size of the shapes.In addition, an easily comprehensible unit (e.g. a distance such as mm)can be provided. This can be useful in certain applications like medicalimaging and determining the shape of an organ, where the error of ashape outline (in pixels or mm, for example) can be more useful than anaccuracy percentage.

D. Hausdorff Distance

Another method for comparing shapes is the Hausdorff distancemeasurement. The Hausdorff distance is the maximum distance between theborders of two shapes.

FIG. 2 shows an example of a Hausdorff distance measurement. Tocalculate the Hausdorff distance, the shortest distances to shape X fromeach specific point on shape Y are identified. In FIG. 2, a Hausdorffdistance is shown by line 210. Line 210 shows that shortest distancebetween point 205 (on shape Y) and shape X is a straight line to point207 on shape X.

The shortest distances to shape Y from each specific point on shape Xare also identified. Line 220 shows the shortest distance between point215 (on shape X) and shape Y is a straight line to point 217 on shape Y.As line 210 is larger than line 220, line 210 corresponds to theHausdorff distance since it is the maximum of the identified shortestdistances. Two shapes are considered to match well if they have a shortHausdorff distance.

A drawback of the Hausdorff distance is the dependency on a maximumdistance. One outlier can dominate the comparison measure. If two shapesare nearly identical except for one outlying point or region, a largeHausdorff distance will still result and the shapes may be considered avery poor match. Further, the Hausdorff distance is not immediatelyevident, and locating it may require extensive analysis and measurement.

In contrast to the Hausdorff distance measurement, embodiments can betopology-independent and not dramatically affected by outlying points.In some embodiments, it is not necessary to identify a point from thefirst shape that corresponds to a point from the second shape.Accordingly, embodiments can provide a more accurate shape comparisontool, and be easier and faster to execute.

II. Shape Similarity

To determine a similarity between shapes, embodiments can be determiningusing an intersection shape and a union shape. These shapes are the samewhen the two shape-determining processes provide identical shapes. Adifference between the intersection shape and the union shape is thusused to determine a similarity metric.

A. Difference of Union and Intersection

To determine the intersection shape and the union shape, the two shapescan be superimposing onto a same coordinate space. Once the two shapesare in the same coordinate space, a difference between the intersectionshape and the union shape can be determined. The difference can bedetermined as a distance. For example, the average distance between theunion shape and the intersection shape can be determined as thedifference. Thus, the measurement of shape difference can be given as ametric with a unit of distance (e.g. cm or mm).

FIG. 3 shows an approximation for calculating a difference between twoshapes according to embodiments of the present invention. The example ofFIG. 3 is in two dimensions. A first shape 311 and a second shape 312are superimposed in diagram 310. The two shapes 311, 312 are put into asame coordinate space. This may occur automatically as the two shapesmay be defined from a same image, and thus the boundaries of the twoshapes already exist in a same coordinate space, i.e., defined withrespect to a same origin.

An intersection shape 315 corresponds to the intersection of the twoshapes. A union shape 316 corresponds to the union of the two shapes.Union shape 316 includes intersection shape 315 and severalnon-overlapping striped regions 318. The non-overlapping regions arestriped with arrows, while the intersection region is left blank.

Diagram 320 highlights the intersection area, represented by A_(I), ingray. The union area (or the total area of the first and second shapescombined) is the entire area enclosed by the bolded outer boundary. Theunion area is represented by A_(U). Area is used for thistwo-dimensional example.

The difference between the two shapes can be represented by the averagedistance between union area and the intersection area. To make thecalculation of the average distance easier, the absolute value of theareas can be utilized. To demonstrate this point, the intersection shapeand the union shape are respectively approximated as concentric circles335 and 336 in diagram 330. The intersection area A_(I), still havingthe same value/magnitude, is redrawn as circle 335. The union area A_(U)also has the same value and is redrawn as circle 336. Redrawing theshapes in 320 as the circles in 330 give approximately the same outcome,and help to illustrate the use of the difference in the areas A_(U) andA_(I), to obtain a similarity metric.

The distance between the borders of two concentric circles 335, 336 isthe same at every point, and is just the difference between the radii.Accordingly, the average distance between the union area and theintersection area is just the difference between the radii, as shown indiagram 330:d=r _(U) −r _(I)

Redrawing the shapes as circles is helpful because the area of a circleis a simple formula that is dependent on a distance (A=πr²). The formulacan be rearranged so that the radius is defined in terms of the area

$\left( {r = \sqrt{\frac{A}{\pi}}} \right).$Now, the area can be substituted for the radius in the above equation,creating a new equation that is more easily applied to non-circularshapes:

$\overset{\_}{d} = {{r_{U} - r_{I}} = {\frac{1}{\sqrt{\pi}}\left( {\sqrt{A_{U}} - \sqrt{A_{I}}} \right)}}$

The above equation was derived using the formula for the area of acircle, so the exact formula will be slightly different for othershapes. Specifically, the normalization factor

$\frac{1}{\sqrt{\pi}}$will be different. This will be explained in detail further below.

In order to determine the average distance between the union shape andintersection shape of any two shapes, the union area and intersectionarea need to be determined (as well as a normalization factor). This canbe easier than directly measuring and averaging the distances at eachpoint, although such a technique can be used. An area can be determinedvia a number of techniques, such as counting the pixels contained withinthe borders of the area or volume.

B. Method

FIG. 4 is a flowchart illustrating a method 400 for determining anaccuracy of shape-determining processes for identifying shapes of a bodytissue in one or more images of a patient according to embodiments ofthe present invention. The method can compare any two-dimensional orthree-dimensional shapes. The shapes may be shapes of a body tissuebased on one or more images, including shapes of a body tissue based ona surface scan of a reflected spectrum. The one or more images and otherimages mentioned herein can be diagnostic image(s), such as CT, Mill,and the like. The comparison of the shapes can be used to identify theaccuracy of a shape-determining process, thereby allowing improvement ofthe shape determining process by determining when accuracy has improved.

In block 410, first data is received that defines a first boundary of afirst shape of a body tissue in at least a portion of the one or moreimages. The first shape may be determined by a first shape-determiningprocess (e.g., an algorithm), and the first shape-determining processmay be a standard, respected process (e.g. image analysis by an expertradiologist). Accordingly, the first shape may be a reference acceptedas an accurate representation of the true body tissue shape. The datadefining the boundary of the shape may be defined as a set of pixels inone or more images, a set of coordinates, or any other suitable data.The boundary can be in two dimensions or three dimensions depending onwhether the shape is two-dimensional or three-dimensional.

In block 420, second data is received that defines a second boundary ofa second shape of the body tissue in at least a portion of the one ormore images. The second shape may be determined by a secondshape-determining process, and the second shape-determining process maybe a new or alternative process (e.g. a new computer analysisalgorithm). The second shape may be similar to or very different thanthe first shape. The accuracy of the second shape-determining processmay depend on how similar the second shape is to the first shape. Thedata defining the boundary of the shape may be any suitable data, e.g.,as described herein.

In block 430, the first shape and the second shape may be placed withina coordinate space. In embodiments, the first shape and second shape mayboth have been determined from one image, and the first shape and secondshape may be shown on the original image. A common reference point (e.g.a marker or other biological tissue) in the image may be used to overlaythe first shape and second shape appropriately. Other methods forcorrectly overlaying the first shape and second shape may be used, suchas placing the centers of both the first shape and second shape at thesame point. As another example, a same reference point can be determinedin two images, and shapes can be defined with respect to that samereference point.

In block 440, an intersection shape of the first shape and second shapein the coordinate space may be determined. The intersection shape may bedetermined manually or automatically by a computer system. Theintersection shape can include the area where both the first shape andthe second shape are present. A boundary of the intersection shape maybe shown and/or highlighted. The boundary of the intersection shape maybe comprised of various segments of the outlines of the first shape andthe second shape as the first and second boundaries cross each other.Further, the area of the intersection shape may be determined. Forexample, the area may be determined by counting the pixels within theintersection shape, by counting larger blocks within the intersectionshape, by using the curve given by the boundary of the intersectionshape, or by any other suitable method.

In block 450, a union shape of the first shape and second shape in thecoordinate space may be determined. The union shape may be determinedmanually or automatically by a computer system. The union shape caninclude the area where either the first shape or the second shape ispresent. A boundary of the union shape may be shown. The boundary may becomprised by various segments of the boundaries of the first shape andthe second shape. The boundary of the union shape may define acombination shape formed by the overlaying of the first shape and secondshape. Further, the area of the union shape may be determined, e.g., asdescribed herein.

In block 460, the difference between the union shape and theintersection shape may be calculated. In some embodiments, thedifference may be represented by a distance, where the distancecorresponds to an average distance between the outline of theintersection shape and the outline of the union shape. The averagedistance may be calculated by a formula, and the formula may be based onthe values of the areas of the union shape and the intersection shape.In various embodiments, the difference may alternatively be a differencein area, a difference in the square roots of the areas, a measurement ofthe percentage of the union shape that is filled by the intersectionshape, or any other suitable value or metric. The difference may becalculated manually or calculated automatically by a computer system.

The value of the difference between the union shape and the intersectionshape may be used to compute a shape similarity metric. The shapesimilarity metric may be the same as the difference value, or it may bebased on the difference value. For example, the shape similarity metricmay be the difference value multiplied by a normalization factor.

In some embodiments, the difference between the union shape and theintersection shape may be calculated by computing an intersection sizeof the intersection shape and a union size of the union shape. Theintersection size can be subtracted from the union size to obtain thedifference.

In block 470, the shape similarity metric can be provided. The accuracyof the second shape-determining process may be determined based on theshape similarity metric. In embodiments, the second shape-determiningprocess may be deemed accurate if it can produce a second shape similarto the first shape produced by the first shape-determining process. Forexample, the metric may indicate that the second shape-determiningprocess was accurate if the average distance between the union shape andintersection shape was small, or if the second shape is otherwisesimilar to the first shape.

Embodiments can determine a distance metric (e.g. the average distancebetween the intersection shape boundary and the union shape boundary)instead of a proportional difference. Accordingly, if a distance metricvalue is determined for a comparison of two smaller shapes and anotherdistance metric value is determined for a comparison of two largershapes, the two distance metric values can be similar if the differencesbetween the intersection shapes and the union shapes are similar.

Embodiments can compare three-dimensional shapes by breaking downthree-dimensional shapes into a number of two-dimensional (2D) slices.For example, embodiments can compare corresponding 2D slices from areference three-dimensional shape and a test three-dimensional shape.Corresponding 2D slices can be determined based on a scan, as manyimaging techniques perform 2D scans and create a 3D image from the 2Dscans. A shape similarity metric (e.g. average distance) can bedetermined for each slice comparison, and a total shape similaritymetric can be determined by averaging the slice-specific shapesimilarity metrics. The slices may be different sizes, so the averagemay be weighted accordingly. For example, slices of greater area orcircumference may be given more weight when averaging. In anotherembodiment, the shape similarity metrics are not dependent on size, andare not weighted differently.

In other embodiments, the shape similarity metric can be used todetermine the most similar atlas(es) for a given patient image. In oneimplementation, this determination can be made based on a comparison ofthe body contour of the patient with the body contour of the atlases insome region of interest. For example, the body contour can be for a leg,an arm, a torso, a hand, a foot, and other body contours. Finding asimilar atlas can be important to obtain reasonable segmentationresults. For example, an atlas can be used to segment the image intodifferent body tissues, and thus a similar atlas can be important toaccurately identify a shape of a body tissue. Comparisons of multiplebody contours can be used to determine the most similar atlas(es).

Further examples for using the shape similarity metric are as follows.The shape similarity metric can be used in searching knowledgedatabases, e.g., to find a similar target volume or organ shape in adatabase of patients already treated. Once the similar target volume ororgan shape is identified, information about the similar shape can beused for a current patient. For example, a treatment plan for the otherpatient can be used for the current patient.

The shape similarity metric can be used in checking quality of manualcontouring by doing a quick check with an average shape or one predictedby statistics. Such a process could be used in training, e.g., forimproving the manual contouring skill of a radiologist.

The shape similarity metric can be used for training model-based methodswhen there is a need to tune parameters of a model for it to bestpredict the shape of a certain organ.

III. Determining Intersection and Union

A shape in an image can be defined by boundary outlines. In oneimplementation, the boundaries can be represented by a function. Inanother implementation, a shape boundary can be defined by a set ofpixels within the shape boundaries. A size (e.g., area or volume) of ashape can be determined by identifying the number of pixels within theshape. An absolute value can be obtained by knowing the scale for apixel size. Alternatively, the size of the shape can be determined byintegrating the function that defines the shape boundaries, e.g.,counting blocks within the boundary.

A. Intersection

In two dimensions, the intersection of two shapes can be defined as thearea where both shapes are present. In embodiments, the intersection canbe determined by identifying the pixels that are associated with both ofthe two shapes. These pixels can then be associated with theintersection shape. The boundary of the intersection can includesegments of the outlines of both shapes. Accordingly, the intersectionoutline can be determined by tracing or highlighting the outline ofeither the first shape or second shape, whichever outline is inside theother, e.g., closer to a center point.

B. Union

The union of two shapes can be defined as the combination of the twoshapes. In embodiments, the intersection can be determined byidentifying the pixels that are associated with either of the twoshapes. These pixels can then be associated with the union shape. Forexample, referring back to FIG. 3, the striped regions 318 of diagrams310-330 contain the pixels that are within one shape, while the grayregions contain the pixels that are within both shapes. The union areais the combination of both the gray and striped areas, and the outlineof the union area is bolded in diagram 320 and diagram 330.Alternatively, an image with overlapped shapes can be analyzed, and theunion area can be manually identified. The outline of the union caninclude segments of the outlines of both shapes. Accordingly, the unionboundary can be determined by tracing or highlighting the boundary ofeither the first shape or second shape, whichever outline is furtherfrom the center at that point.

C. Circumference and Surface Area

The circumference of a shape is used in some embodiments to determinethe similarity metric. The circumference can be determined using similarinformation as the area/volumes. For example, pixels that define aboundary of a shape can be counted and a scale of a pixel used todetermine circumference. If the shape was defined with a function, thefunction can be used to determine the circumference. Forthree-dimensional shapes, the surface area of a shape can be determinedin a similar manner.

IV. Calculating Difference

As mentioned above, various embodiments can compute the differencebetween the union shape and the intersection shape using selected pointsor by determining an area/volume. The use of areas/volumes can providecertain advantages, such as accuracy and ease of computation.

A. Average of Separate Distance Values

There are multiple ways to determine the average distance between aunion shape and an intersection shape. For example, several measurementsof the distance between the union shape and intersection shape can betaken at different points, and then the measurements can be averaged.Referring back to FIG. 3, the striped regions 318 in diagrams 310, 320,and 330 are striped by a number of arrows. These arrows can be specificmeasured distances between the union shape and the intersection shapethat can be averaged to determine the average distance. As shown, asampling of distances can be measured instead of measuring the distancebetween every pair of corresponding points between the union shape andintersection shape. The distance can be measured for every point on theintersection outline along a given interval (e.g. every tenth pixelalong the intersection outline or a point every 2 mm along theintersection outline).

Measuring and averaging several specific distances can have a number ofdrawbacks. For example, it can be a laborious and imprecise process.Measurements are taken between two specific points on the intersectionboundary and the union boundary, but it may be unclear which point onthe union boundary corresponds to any given point on the intersectionboundary, and vice versa. In some embodiments, for a selected point onthe intersection boundary, the closest point on the union boundary istaken as the corresponding point. Corresponding points may be the samepoint or area on the organ (just shown in a different position), or theymay simply be nearby points used for calculating the distance.

In some embodiments, instead of choosing the closest point, acorresponding point on the union boundary may always be in a certaindirection or location relative a selected point on the intersectionoutline. For example, a center of the union shape can be determined(e.g. a center of mass), and a corresponding point on the union boundarymay be found radially outward from a selected point on the intersectionboundary, directly away from the center. In another example, thedistance may be measured from a selected point on the intersectionboundary to a point on the union outline that is found 45 degrees fromthe horizontal (either in the first quadrant or in the third quadrant).A number of other methods can be used for identifying correspondingpoints.

B. Determining Area

Areas and volumes can be used to determine the difference between theunion and intersection shapes. There are various ways to determine theareas of a union shape and an intersection shape. Methods fordetermining the boundaries and/or pixels of a union shape and anintersection shape are described above. Once the boundary of a shape isknown and/or the pixels within the shape are known, the boundary can beintegrated and/or the pixels can be summed. Numerical integration ormanual counting can be used. In embodiments, there may be an uncertaintyin the boundary lines of a shape (e.g. ±4 mm). In this case, the valueof the area may be given with a corresponding uncertainty value (e.g.±16 mm²).

An image containing a shape can be calibrated in order to determine thesize of a shape distance units (e.g. cm or mm). For example, a referenceobject of known size may be included in the object. The area of thereference object in the image can be determined (e.g. the number ofpixels used for the reference object or the scaled length and height ofthe object in the image), and a scaling factor for the image can bedetermined based on the true size of the reference object and the imagesize of the reference object. In some embodiments, a size (e.g. length,width, or area) per pixel may be determined. A scale may be determined(e.g. 2 cm in image=10 cm in reality), and the scale may be displayed onthe image.

Once a scale is determined, the actual areas of the intersection shapeand union shape can be determined (although area/volume in units ofpixels can be used). If the pixels contained in the shapes have beendetermined and the scale is a known size per pixel (e.g. 2 mm²/pixel),the area of a shape (in pixel units) can be multiplied by the scale tofind the true area of the shape (in mm² units). With shape areas givenin real-world distance units, the average distance between theintersection shape and union shape can be determined in real-worlddistance units.

As explained above, the average distance can be determined based on theareas of the intersection shape and the union shape. Specifically, theformula below can be used. For the circle example, the factor

$\frac{1}{\sqrt{\pi}}$was used. This shape-dependent factor can be generally referred to as anormalization factor k, where the similarity metric is provided by:d=k(√{square root over (A_(U))}−√{square root over (A_(I))}), whereA_(U)=union area, A_(I)=intersection area. Methods for determining kvalues for any shape are discussed below.

C. Area Vs. Average Distance

In some situations, it can be difficult to directly measure the averagedistance using a distance between corresponding points. It can beunclear which points of one shape correspond to which points of acompared shaped. Similarly, it can be unclear which point of a unionshape corresponds to a selected point on an intersection shape. FIG. 5shows an example where it is unclear how to match points on two shapes.The shapes have dissimilar curvature in some areas, and some parts ofthe outline are not close. If corresponding points cannot be identified,the distance between the shapes cannot be accurately measured.

As explained above, the closest point on the union outline can be takenas the corresponding point to an intersection shape, or there may be apreferred direction for measurement. However, the points found withthese methods may not provide actual corresponding points. For example,some forms of curvature can result in the corresponding point actuallybeing the further point away.

Accordingly, using the areas of the shapes to determine the averagedistance can be an easier and more reliable method. Calculating viaareas is often more accurate, easy, and fast when shapeoutlines/contours are larger and more complex. Also, in practice, smallshape areas often have dramatic curves and changes in topology, socalculating average distance via areas can be better suited in thosesituations as well.

In another example, calculating via area can be used in situations wheretwo shapes are being compared against one shape (or other mismatchednumbers of shapes are being compared). For example, one doctor may drawan outline of two connected bones using one continuous outline (i.e. oneshape). Another doctor may draw two separate outlines for the two bones.Distances cannot be directly measured because corresponding pointscannot be accurately determined between one shape and a correspondingset of two shapes. Instead, the group of two outlines can be consideredto be one shape, and their areas can be added. The overlap between theareas of the one shape (first drawing) and the area of the two shapes(second drawing) can still be calculated. Accordingly, the intersectionarea and the union area can still be calculated. Thus, the areas of theshapes can be used to compare the quality of the doctors' drawings.

D. Other Contexts

The shape comparison measurement and shape similarity metric can be usedin a number of contexts. Body tissue imaging is primarily discussedherein, but the embodiments can be applied to any context where2-dimensional or 3-dimensional shapes (especially natural shapes) arecompared. The method can be used where any kind of deformation analysisis taking place, or where a change of shape is observed. Embodiments canbe especially useful where one is interested in producing aninterpretable unit (e.g. a distance metric). For example, embodimentscan be applied to pathology imaging, surgery planning, geographicinformation systems, meteorology, astronomy, remote sensing, and anyother suitable application.

Embodiments can be extended to 4-dimensional shape comparisons as well.For example, an average distance for a changing 3-dimensional shape canbe determined once per a given time interval (e.g. a distance can bedetermined for every 5 seconds), and then the measurements can beaveraged.

Some embodiments can be independent of shape location, and thus shapescan be compared that do not overlap at all. For example, the difference(average distance) of two identical circles would be zero (i.e. they aremeasured to be identical) even if they are in entirely differentlocations.

V. Computing Similarity Metric

As described herein, the shape similarity metric can be the differencevalue, but can also include a normalization factor. In one aspect, thenormalization factor can compensate for different shapes, so that thesimilarity can be consistently determined. For example, one shape mightbe circular, but the other shape might be oblong, and a strictcomparison of areas might provide inconsistent results. Thus, thenormalization factor is based on a property of the shapes, such as acircumference or surface area, which can convey information about asize, form, shape factor, or curvature of a shape.

A. Normalization Factor (Circle)

Referring back to FIG. 3, it was found the average distance can be givenby the formula:

$\overset{\_}{d} = {{r_{U} - r_{I}} = {\frac{1}{\sqrt{\pi}}\left( {\sqrt{A_{U}} - \sqrt{A_{I}}} \right)}}$

Accordingly, the normalization factor for a circle is

$\frac{1}{\sqrt{\pi}}.$The square root is taken of the areas, which results in a dimension ofdistance. In other embodiments, the area can be used with an exponent of1, or other value.

B. Normalization Factor (General)

For non-circular shapes, a different factor k that depends on the shapeis introduced: d=k(√{square root over (A_(U))}−√{square root over(A_(I))}), where A_(U)=union area, A_(I)=intersection area.

An analysis of a large number of human organ contours has shown that kcan be well approximated with the formula:

${{k \approx {\frac{2\sqrt{A}}{C}\mspace{14mu} A}} = {area}},{C = {circumference}}$

This approximation treats random shapes similarly to a circle, andexperimental results have shown that it is a very good approximationthat is suitable for practical uses. In this formula, k is based on thearea and circumference of the original shape (not the intersection shapeor union shape). Methods for determining the area and circumference ofshape were discussed above. Thus, if these quantities are known, anapproximation of the normalization factor k can be determined. Since thesimilarity metric is based on k and the area values, the similaritymetric can be determined for any compared shapes based on the areas andthe circumferences of the original shapes and the areas of theintersection shape and union shape.

The above approximation for the normalization factor k can be tested byplugging in the formulas for the area and circumference of a circle(A=πr², C=2πr). The square root of the area reduces so that thenumerator is 2√{square root over (π)}r, and the denominator of 2πrcancels the 2 and r in the numerator. With the radius variableeliminated and constants reduced, only the constant

$\sqrt{\frac{1}{\pi}}$remains. This is the same k value that was determined above forconcentric circles. A more general formula can be determined bysubstituting shape-specific parameters for k.

FIG. 6 shows two shapes with random curvature to illustrate a generaldifference formula according to embodiments of the present invention. Afirst shape 610 and a second shape 620 are shown in a common coordinatespace. The two shapes, when overlaid, create two new shapes: A_(I)=A₁∩A₂and A_(U)=A₁∪A₂. The intersection shape 630 corresponds to points withinboth shapes, and union shape 640 corresponds to points within eithershape. A_(I), as explained above, can be described as the intersectionarea of a first shape A₁ and a second shape A₂. A_(U), as explainedabove, can be described as the union area of the first shape A₁ and thesecond shape A₂.

Two parameters for each shape, A₁ and A₂, are considered: A_(i)=area andC_(i)=circumference.

When comparing two different shapes, the normalization factor k can beequal to the average of the normalization factors k from each of the twoshapes. Thus, a general k for comparing two shapes is:

$k = {\frac{k_{1} + k_{2}}{2} \approx \left( {\frac{\sqrt{A_{1}}}{C_{1}} + \frac{\sqrt{A_{2}}}{C_{2}}} \right)}$A_(1/2) = area, C_(1/2) = circumference

Accordingly, substituting this general k provides a generalized formulafor the average distance between the union shape and intersection shape(where the union shape and intersection shape are based on twooverlapping shapes):

$\begin{matrix}{\overset{\_}{d} = {{\frac{k_{1} + k_{2}}{2}\left( {\sqrt{A_{U}} - \sqrt{A_{I}}} \right)} = {\frac{\left( {\frac{2\sqrt{A_{1}}}{C_{1}} + \frac{2\sqrt{A_{2}}}{C_{2}}} \right)}{2}\left( {\sqrt{A_{U}} - \sqrt{A_{I}}} \right)}}} \\{= {\left( {\frac{\sqrt{A_{1}}}{C_{1}} + \frac{\sqrt{A_{2}}}{C_{2}}} \right)\left( {\sqrt{A_{U}} - \sqrt{A_{I}}} \right)}}\end{matrix}$

Written plainly, the formula for the difference between two overlappedshapes is given by:

$\overset{\_}{d} = {\left( {\frac{\sqrt{A_{1}}}{C_{1}} + \frac{\sqrt{A_{2}}}{C_{2}}} \right)\left( {\sqrt{A_{U}} - \sqrt{A_{I}}} \right)}$VI. Single or Non-Overlapping Shapes

Embodiments can also be applied to scenarios where the two shapes arenot overlapping, which can include when one shape does not exist. Insuch situations, the similarity may be quite large, but at least ametric can be obtained. And, the high value can be a signal thatsomething has gone wrong.

A. Single Shape

When comparing two shapes, sometimes only one shape will be present.This may happen when one of the shape-determining processes malfunctionsor is very inaccurate. A shape-determining process may falsely determinethat there is no shape when there actually is a shape, it may determinethat there is a shape when there actually is no shape, it may determinethat the shape location is elsewhere (e.g. out of the image area), or itmay determine that the shape is small enough to degenerate to a singlepoint with an effective area of zero.

In the case of a single shape, there is no value for the second area andcircumference (or the area and circumference can both be taken as zero).It follows that the union area is just the area of the single shape, andthe intersection area is zero. The normalization factor is dependent onthe shapes, e.g., an inverse of a circumference. Since there is only oneshape (not two different shapes), the normalization factor is expressedas:

$k \approx \frac{2\sqrt{A}}{C}$

Accordingly, the difference formula is reduced as follows:

$\overset{\_}{d} = {{\frac{2\sqrt{A}}{C}\sqrt{A}} = \frac{2A}{C}}$

Thus, for a single shape that is being compared to a non-existent shape,the formula is reduced to:

$\overset{\_}{d} = \frac{2A}{C}$

For a single shape that is a circle,

$\overset{\_}{d} = \frac{2A}{C}$reduces to d=r, the difference from the boundary of the shape to thecenter. This distance is greater than any possible average distance thatcould result from having another shape that is smaller than the presentshape, which demonstrates that there indeed was a poor match (a realshape is not very similar to a non-existent shape).

B. Non-Overlapping Shapes

For some measurements, two shapes will be present but non-overlapping.Since the two shapes do not overlap, they are considered to bedifferent, non-corresponding shapes. In this case, the similarity metricfor each individual shape can be interpreted as the average distancefrom the boundary to the center of the shape (i.e. the average radius).In order to transform the shape into a point, the outline of the contourneeds to be moved by this average distance. If one shape weretransformed into a point, the single-shape scenario (discussed above)would occur. Accordingly, for non-overlapping shapes, the averagedistance can be calculated for each shape separately as if it were asingle-shape scenario (as shown above), and the average distance for theunion shape can be interpreted as the average of the two single-shapedistances. The formula is derived as follows:

$\overset{\_}{d} = {\frac{{\overset{\_}{d}}_{1} + {\overset{\_}{d}}_{2}}{2} = {\frac{\left( {\frac{2A_{1}}{C_{1}} + \frac{2A_{2}}{C_{2}}} \right)}{2} = {\frac{A_{1}}{C_{1}} + \frac{A_{2}}{C_{2}}}}}$

For two circles, this formula reduces to

$\overset{\_}{d} = {\frac{r_{1} + r_{2}}{2}.}$Thus, the distance metric for two non-overlapping circles will always besmaller than the distance metric for the larger circle taken as a singleshape. This makes sense, because two non-overlapping shapes are arguablymore similar than any single shape is to a non-existent shape.

C. Method

FIG. 7 is a flowchart illustrating a method 700 for determining anaccuracy of a shape-determining process, where there is no overlappingof shapes according to embodiments of the present invention. Method 700can compare any two-dimensional or three-dimensional shapes. The shapesmay be shapes of a body tissue based on an image, including shapes of abody tissue based on a surface scan of a reflected spectrum or shapesdetermined by any other suitable imaging method. One or more of theblocks or steps in the method may be performed by a computer system.

In block 710, first data is received that defines a first boundary of afirst shape of a body tissue in at least a portion of the one or moreimages. Block 710 may be performed in a similar manner as describedabove. For example, the first shape may be determined by a firstshape-determining process, and the first shape-determining process maybe a standard, respected process (e.g. image analysis by an expertradiologist). Accordingly, the first shape may be a reference acceptedas an accurate representation of the true body tissue shape.Alternatively, the first shape may be a new or alternative process (e.g.a new computer analysis algorithm). The data defining the boundary ofthe shape may be an image, a set of coordinates, or any other suitabledata.

In block 720, it may be determined that the first shape does notintersect with a second shape. For example, there may not be any othershapes, or another shape may be located elsewhere within or outside ofan image or coordinate space. If there is another shape, it may bedetermined that no image pixels are associated with both shapes, or itmay be determined that the curves defined by the boundaries of theshapes do not intersect.

In block 730, a shape similarity metric may be computed. The shapesimilarity metric may be computed by determining a size of the firstshape. The size of may be determined by multiplying an area or volume ofthe first shape by a normalization factor for the shape. For example,the area of the shape may be found by determining the number of pixelswithin the area, and the area may be multiplied by a scaling factor togive the size of the shape in real-world units.

If the size is an area, the square root of the area may be determined,and the result may be multiplied by a constant based on the shape (e.g.

$\sqrt{\frac{1}{\pi}}$for a circle). The result may be another size with distance units (e.g.cm or mm), which may be the shape similarity metric. In someembodiments, the shape similarity metric may be the same as the size, orit may be based on the size (e.g. the shape similarity metric may be thesize multiplied by a normalization factor). Any suitable formula may beused in determining the size and/or the shape similarity metric, and aformula may be based on the shape, e.g., as described above.

In some embodiments, a second shape does exist. In such an embodiment,second data defines a second boundary of the second shape of the bodytissue. The second shape can be determined by a second shape-determiningprocess. The first shape and the second shape can be placed within acoordinate space. The shape similarity metric can be computed bydetermining a second size of the second shape. The second size can bedetermined by a multiplication of an area or a volume of the secondshape by a second normalization factor for the second shape. A sumincluding the first size and the second size can then be computed.

In block 740, the shape similarity metric is provided. An accuracy ofthe first shape-determining process may be determined based on the shapesimilarity metric. In embodiments, a lesser shape similarity metric canindicate a more accurate first shape-determining process. Embodimentscan determine a distance metric instead of a proportion metric.Accordingly, the metric can have values other than zero. The shapesimilarity metric for the first shape and the second shape to anothershape similarity metric of a different pair of shapes for determining arelative accuracy.

Embodiments can also analyze three-dimensional shapes by breaking downthree-dimensional shapes into a number of two-dimensional slices. Ashape similarity metric (e.g. distance) can be determined for each slicecomparison, and a total shape similarity metric can be determined byaveraging the slice-specific shape similarity metrics. The slices may bedifferent sizes, so the average may be weighted accordingly. Forexample, slices of greater area or circumference may be given moreweight when averaging.

VII. Identifying Treatments Information for Similar Patients

The similarity metric can also be used to identify similar body tissues(organs or tumors) in other patients, and then use treatment informationfrom a patient with a similar body tissue.

FIG. 8 is a flowchart illustrating a method 800 of comparing shapes ofbody tissues in images of patients according to embodiments of thepresent invention. Method 800 can be performed. Method 800 can compareany two-dimensional or three-dimensional shapes of various patients. Theshapes may be shapes of body tissues based on images, including shapesof body tissues based on surface scans of reflected spectrums or shapesdetermined by any other suitable imaging method. One or more of theblocks or steps in the method may be performed by a computer system.

At block 810, first data is received that defines a first boundary of afirst shape of a first body tissue of a first patient. Block 810 may beperformed in a similar manner as block 410 of FIG. 4. The first data canbe determined based on one or more images of the first patent.

Blocks 820-860 can be performed for each of a plurality of secondpatients.

At block 820, second data is received that defines a second boundary ofa second shape of a second body tissue of one of the plurality of secondpatients. The first shape and the second shapes can be determined usinga same shape-determining process or different same shape-determiningprocesses. Block 820 may be performed in a similar manner as block 420of FIG. 4. The second data can be determined based on one or more imagesof the one of the plurality of second patients.

At block 830, the first shape and the second shape may be placed withina coordinate space. Block 830 may be performed in a similar manner asblock 430 of FIG. 4. Placing the first shape and the second shape withinthe coordinate space may include aligning the first shape and the secondshape. For example, the center of mass of each can be aligned. In otherembodiments, the objects can be aligned to another point of reference,e.g., a particular body part, such as a spine. An alignment to a bodyoutline can also be performed.

At block 840, an intersection shape of the first shape and second shapein the coordinate space may be determined. Block 840 may be performed ina similar manner as block 440 of FIG. 4.

At block 850, a union shape of the first shape and second shape in thecoordinate space may be determined in the coordinate space. Block 850may be performed in a similar manner as block 450 of FIG. 4.

At block 860, the difference between the union shape and theintersection shape may be calculated, and the value of the differencebetween the union shape and the intersection shape may be used tocompute a shape similarity metric for the given second patient. Block860 may be performed in a similar manner as block 460 of FIG. 4.

At block 870, a first shape similarity metric is identified thatsatisfies one or more criteria. The first shape similarity metriccorresponds to a particular second patient. The first body tissue andthe second body tissues are of a same type. For example, the two bodytissues may both be a particular organ, such as a liver, heart, orbrain. As another example, the two body tissues may be both be a tumor,which may be in contact to a same type of organ.

In one example, the one or more criteria can specify that the highestshape similarity metric is to be selected. In another example, a set ofthe shape similarity metrics of the plurality of second patients thatsatisfy the one or more criteria can be identified. For instance, theone or more criteria can include a threshold value for the shapesimilarity metrics, and the set would correspond to the shape similaritymetrics that exceed the threshold value. The first shape similaritymetric can be selected from the set of the shape similarity metrics.Such a selection can include identifying the particular second patientcorresponding to the first shape similarity metric based on treatmentoutcomes for the second patients whose shape similarity metrics satisfythe one or more criteria.

At block 880, treatment information for the particular second patient isretrieved for use in determining a treatment plan for the first patient.Since the corresponding second patient is known for each of thesimilarity metrics, the particular second patient can be determined forthe first shape similarity metric. For example, each second patient canhave a patient ID, and that patient ID can be stored in association witheach similarity metric. When the first similarity metric is chosen, thecorresponding patient ID can be used to retrieve the treatmentinformation for the particular second patient, e.g., using a databasequery using the patient ID.

As examples, the treatment information can include one or more of: ageometry of a radiation beam, a dosage of the radiation beam, and anumber of sessions for treatment using the radiation beam. When thefirst body tissue is a tumor, the treatment information can prescribehow radiation is to be applied to the tumor.

Embodiments can also determine the treatment plan for the first patientbased on the treatment information. For example, the values from theother patient can be used as an initial value in an optimizationprocess, e.g., as described in U.S. Patent Application Publication2015/0095044 entitled “Decision Support Tool For Choosing TreatmentPlans,” by Hartman et al.; and U.S. Patent Application Publication2015/0095043 entitled “Automatic Creation And Selection Of DosePrediction Models For Treatment Plans” by Cordero Marcos et al, whichare incorporated by reference in their entirety. Embodiments can alsoperform the treatment plan using a radiation beam.

In some embodiments, similarity metrics can be determined for multipleorgans/tumors. And, a statistical value for the similarity metrics canbe used to select a second patient that corresponds to the firstpatient. For example, an average or sum of the similarity metrics can beused to determine an optimal second patient whose treatment informationcan be used to determine a treatment plan for the first patient.

As an example of method 800, a new patient can be scanned and a shapecan be determined for the patient's liver. The shape can then becompared to a database of liver shapes for patients who have had atreatment plan determined, and who may have had at some treatmentalready. A top similarity metric can be determined for a liver in thedatabase. The top similarity metric may be the very highest or satisfysome criteria, such as top 5% or within a specified amount of thehighest, and the like.

An outcome of patients can also be used. For example, a group ofpatients that have a similarity metric above a threshold can beidentified. And, a patient with the best outcome can be selected.Treatment information can then be determined for the selected liver inthe database.

Examples of such treatment information are as follows. The geometry ofthe radiation beam can be used to determine how to miss an organ or howto focus on a tumor. The dosage can be used to ensure a sufficientdosage is used to kill the tumor and not damage organs. The dosage couldbe a mean dosage and a volumetric dosage. A number of sessions(fractions) of treatment can be specific for the treatment informationof the other patient. Once the treatment information is obtained fromthe similar patient, the treatment information can be used to tailor atreatment plan for the specific patient.

VIII. Three-Dimensional

It may be desirable to compare two shapes that are three-dimensional. Ananalogous similarity metric can be provided to describe the differencebetween the shapes. The shapes can be superimposed on the samecoordinate space, and an intersection volume and union volume can bedetermined. Accordingly, an average distance from the surface area ofthe intersection volume to the surface area of the union volume can bedetermined.

As described above, the above-described method for determining thedifference between two-dimensional shapes can be extended into threedimensions. A three-dimensional shape can by separated into a number oftwo-dimensional shapes, or slices. The slices each have a certain areaand, when stacked, can re-create the original three dimensional shapewith a certain volume. For example, a CT scan can produce a number oftwo-dimensional slices that represent a three-dimensional shape. A shapesimilarity metric (e.g. average distance) can be determined for eachslice comparison, and a total shape similarity metric can be determinedby averaging the slice-specific shape similarity metrics. The slices maybe different sizes, so the average may be weighted accordingly. Forexample, slices of greater area or circumference may be given moreweight when averaging.

Alternatively, two-dimensional slices can be used to determine thevolume of a three-dimensional shape. The area of each slice can bedetermined as described above (e.g. counting pixels), and the volume canbe determined by multiplying the total area of all the slices by thethickness of each slice. Knowing the volume, a formula for comparingthree-dimensional shapes that is analogous to the above-describedformula can be used.

The volume of a three-dimensional shape is associated with the radius ofthe shape, similarly to how the area of a two-dimensional shape isassociated with the radius. For example, for a circle, A=πr², and for asphere (the three-dimensional extension of a circle),

$V = {\frac{4}{3}\pi\;{r^{3}.}}$The radius of a sphere can be written as:

$r = \sqrt[3]{\frac{3V}{4\pi}\;}$

Alternatively, through a similar derivation process as shown fortwo-dimensional shapes, it can be shown that the distance between thesurface areas of concentric spheres is given by:

$\overset{\_}{d} = {{r_{U} - r_{I}} = {\sqrt[3]{\frac{3}{{4\pi}\;}}\left( {\sqrt[3]{V_{U}} - \sqrt[3]{V_{I}}} \right)}}$

The above formula is similar to the two-dimensional formula, but thecube root of the volume is used instead of the square root of the area,and the normalization factor k is different.

Shown plainly, the formula for calculating the average distance betweenthe surface areas of two three-dimensional, volumetric shapes can begiven by: d=k(³√{square root over (V_(U))}−³√{square root over(V_(I))}), where V_(U)=union volume, V_(I)=intersection volume.

The approximation of the shape-dependent normalization factor k for asingle volumetric shape is given by:

$k \approx \frac{3V^{2/3}}{A}$ V = volume, A = surface  area

This approximation can be tested by substituting in the formulas for thevolume and surface area of a sphere

$\left( {{V = {\frac{4}{3}\pi\; r^{3}}},{A = {4\pi\; r^{2}}}} \right).$The radius variables and constants cancel such that the constant

$\sqrt[3]{\frac{3}{4\pi}}$remains. This is the same k value that was determined above.

Through a process similar to deriving the general two-dimensionalformula, it can be shown that the three-dimensional general formula forthe average distance between any two overlapping shapes is given by:

$\overset{\_}{d} = {{\frac{k_{1} + k_{2}}{2}\left( {\sqrt[3]{V_{U}} - \sqrt[3]{V_{I}}} \right)} = {\frac{3}{2}\left( {\frac{V_{1}^{2/3}}{A_{1}} + \frac{V_{2}^{2/3}}{A_{2\;}}} \right)\left( {\sqrt[3]{V_{U}} - \sqrt[3]{V_{I}}} \right)}}$

The analogous three-dimensional formula for the average distance whenonly a single shape is present and being compared to a non-existingsecond volumetric shape is given by:

$\overset{\_}{d} = \frac{3V}{A}$

The analogous three-dimensional formula for measuring the differencebetween two non-overlapping volumetric shapes is given by:

$\overset{\_}{d} = {\frac{{\overset{\_}{d}}_{1} + {\overset{\_}{d}}_{2}}{2} = {\frac{3}{2\;}\left( {\frac{V_{1}}{A_{1}} + \frac{V_{2}}{A_{2}}} \right)}}$IX. Computer System

Any of the computer systems mentioned herein may utilize any suitablenumber of subsystems. Examples of such subsystems are shown in FIG. 9 incomputer system 10. In some embodiments, a computer system includes asingle computer apparatus, where the subsystems can be the components ofthe computer apparatus. In other embodiments, a computer system caninclude multiple computer apparatuses, each being a subsystem, withinternal components.

The subsystems shown in FIG. 9 are interconnected via a system bus 75.Additional subsystems such as a printer 74, keyboard 78, storagedevice(s) 79, monitor 76, which is coupled to display adapter 82, andothers are shown. Peripherals and input/output (I/O) devices, whichcouple to I/O controller 71, can be connected to the computer system byany number of means known in the art such as input/output (I/O) port 77(e.g., USB, FireWire®). For example, I/O port 77 or external interface81 (e.g. Ethernet, Wi-Fi, etc.) can be used to connect computer system10 to a wide area network such as the Internet, a mouse input device, ora scanner. The interconnection via system bus 75 allows the centralprocessor 73 to communicate with each subsystem and to control theexecution of instructions from system memory 72 or the storage device(s)79 (e.g., a fixed disk, such as a hard drive or optical disk), as wellas the exchange of information between subsystems. The system memory 72and/or the storage device(s) 79 may embody a computer readable medium.Any of the data mentioned herein can be output from one component toanother component and can be output to the user.

A computer system can include a plurality of the same components orsubsystems, e.g., connected together by external interface 81 or by aninternal interface. In some embodiments, computer systems, subsystem, orapparatuses can communicate over a network. In such instances, onecomputer can be considered a client and another computer a server, whereeach can be part of a same computer system. A client and a server caneach include multiple systems, subsystems, or components.

It should be understood that any of the embodiments of the presentinvention can be implemented in the form of control logic using hardware(e.g. an application specific integrated circuit or field programmablegate array) and/or using computer software with a generally programmableprocessor in a modular or integrated manner. As used herein, a processorincludes a multi-core processor on a same integrated chip, or multipleprocessing units on a single circuit board or networked. Based on thedisclosure and teachings provided herein, a person of ordinary skill inthe art will know and appreciate other ways and/or methods to implementembodiments of the present invention using hardware and a combination ofhardware and software.

Any of the software components or functions described in thisapplication may be implemented as software code to be executed by aprocessor using any suitable computer language such as, for example,Java, C, C++, C# or scripting language such as Perl or Python using, forexample, conventional or object-oriented techniques. The software codemay be stored as a series of instructions or commands on a computerreadable medium for storage and/or transmission, suitable media includerandom access memory (RAM), a read only memory (ROM), a magnetic mediumsuch as a hard-drive or a floppy disk, or an optical medium such as acompact disk (CD) or DVD (digital versatile disk), flash memory, and thelike. The computer readable medium may be any combination of suchstorage or transmission devices.

Such programs may also be encoded and transmitted using carrier signalsadapted for transmission via wired, optical, and/or wireless networksconforming to a variety of protocols, including the Internet. As such, acomputer readable medium according to an embodiment of the presentinvention may be created using a data signal encoded with such programs.Computer readable media encoded with the program code may be packagedwith a compatible device or provided separately from other devices(e.g., via Internet download). Any such computer readable medium mayreside on or within a single computer product (e.g. a hard drive, a CD,or an entire computer system), and may be present on or within differentcomputer products within a system or network. A computer system mayinclude a monitor, printer, or other suitable display for providing anyof the results mentioned herein to a user.

Any of the methods described herein may be totally or partiallyperformed with a computer system including one or more processors, whichcan be configured to perform the steps. Thus, embodiments can bedirected to computer systems configured to perform the steps of any ofthe methods described herein, potentially with different componentsperforming a respective steps or a respective group of steps. Althoughpresented as numbered steps, steps of methods herein can be performed ata same time or in a different order. Additionally, portions of thesesteps may be used with portions of other steps from other methods. Also,all or portions of a step may be optional. Additionally, any of thesteps of any of the methods can be performed with modules, circuits, orother means for performing these steps.

The specific details of particular embodiments may be combined in anysuitable manner without departing from the spirit and scope ofembodiments of the invention. However, other embodiments of theinvention may be directed to specific embodiments relating to eachindividual aspect, or specific combinations of these individual aspects.

The above description of exemplary embodiments of the invention has beenpresented for the purposes of illustration and description. It is notintended to be exhaustive or to limit the invention to the precise formdescribed, and many modifications and variations are possible in lightof the teaching above. The embodiments were chosen and described inorder to best explain the principles of the invention and its practicalapplications to thereby enable others skilled in the art to best utilizethe invention in various embodiments and with various modifications asare suited to the particular use contemplated.

A recitation of “a”, “an” or “the” is intended to mean “one or more”unless specifically indicated to the contrary. The use of “or” isintended to mean an “inclusive or,” and not an “exclusive or” unlessspecifically indicated to the contrary.

All patents, patent applications, publications, and descriptionsmentioned here are incorporated by reference in their entirety for allpurposes. None is admitted to be prior art.

What is claimed is:
 1. A method of determining an accuracy ofshape-determining processes for identifying shapes of a body tissue inone or more images of a patient, the method comprising: receiving firstdata that defines a first boundary of a first shape of the body tissuein at least a portion of the one or more images, the first shape beingdetermined by a first shape-determining process; receiving second datathat defines a second boundary of a second shape of the body tissue inat least a portion of the one or more images, the second shape beingdetermined by a second shape-determining process; determining, by acomputer system, an intersection shape of the first shape and the secondshape; determining, by the computer system, a union shape of the firstshape and the second shape; calculating, by the computer system, adifference between the union shape and the intersection shape;computing, by the computer system, a shape similarity metric based onthe difference; and providing the shape similarity metric fordetermining an accuracy of the second shape-determining process relativeto the first shape-determining process.
 2. The method of claim 1,wherein the first data and the second data includes the one or moreimages of the patient, and wherein the method further comprises:determining a reference point in the one or more images, wherein each ofthe one or more images include the reference point; and definingcoordinates of the first shape and the second shape with respect to thereference point.
 3. The method of claim 2, wherein calculating thedifference between the union shape and the intersection shape includes:for each of a plurality of points on the intersection shape: identifyinga corresponding point on the union shape that corresponds to the pointon the intersection shape; and calculating a distance between the pointon the intersection shape and the corresponding point on the unionshape; and computing an average of the distances to obtain thedifference.
 4. The method of claim 1, wherein calculating the differencebetween the union shape and the intersection shape includes: computingan intersection size of the intersection shape; computing a union sizeof the union shape; and subtracting the intersection size from the unionsize to obtain the difference.
 5. The method of claim 4, whereincomputing the shape similarity metric includes: calculating anormalization factor; and multiplying the difference and thenormalization factor to obtain the shape similarity metric.
 6. Themethod of claim 5, wherein the normalization factor is determined basedon a property of the first shape and the second shape.
 7. The method ofclaim 5, wherein computing the intersection size includes taking asquare root of an intersection area of the intersection shape, whereincomputing the union size includes taking the square root of a union areaof the union shape, and wherein the normalization factor includes a sumof: a first term including the square root of a first area of the firstshape divided by a first circumference of the first shape; and a secondterm including the square root of a second area of the second shapedivided by a second circumference of the second shape.
 8. The method ofclaim 5, wherein the first shape is a first two-dimensional slice of thebody tissue, wherein the second shape is a second two-dimensional sliceof the body tissue, the method further comprising: computing shapesimilarity metrics for other slices of the body tissue; and combiningthe shape similarity metrics for the slices to obtain a total shapesimilarity metric.
 9. The method of claim 5, wherein the first shape andthe second shape are three-dimensional, wherein computing theintersection size includes taking a cube root of an intersection volumeof the intersection shape, wherein computing the union size includestaking the cube root of a union volume of the union shape, and whereinthe normalization factor is${\frac{3}{2}\left( {\frac{V_{1}^{2/3}}{A_{1}} + \frac{V_{2}^{2/3}}{A_{2\;}}} \right)},$where V₁ is a first volume of the first shape, V₂ is a second volume ofthe second shape, A₁ is a first surface area of the first shape, and A₂is a second surface area of the second shape.
 10. A method ofdetermining an accuracy of shape-determining processes for identifyingshapes of a body tissue in one or more images of a patient, the methodcomprising: receiving first data that defines a first boundary of afirst shape of the body tissue in at least a portion of the one or moreimages, the first shape being determined by a first shape-determiningprocess; determining, by a computer system, that the first shape doesnot intersect with a second shape; and computing, by the computersystem, a shape similarity metric by: determining a first size of thefirst shape, the first size determined using a first area or a firstvolume of the first shape and a first normalization factor for the firstshape; and using the first size to compute the shape similarity metric.11. The method of claim 10, further comprising: receiving second datathat defines a second boundary of the second shape of the body tissue,the second shape being determined by a second shape-determining process;wherein computing the shape similarity metric further includes:determining a second size of the second shape, the second sizedetermined using a second area or a second volume of the second shapeand a second normalization factor for the second shape; and calculatinga sum including the first size and the second size.
 12. The method ofclaim 11, wherein: the first shape and the second shape aretwo-dimensional and the first normalization factor of the first shapeincludes an inverse of a circumference of the first shape, or the firstshape and the second shape are three-dimensional and the firstnormalization factor of the first shape includes the inverse of asurface area of the first shape.
 13. The method of claim 10, wherein acorresponding second shape does not exist, and wherein: the first shapeis two-dimensional and the shape similarity metric is $\frac{2a}{C}$ where α is an area of the first shape and C is a circumference of thefirst shape, or the first shape is three-dimensional and the shapesimilarity metric is $\frac{3V}{A}$  where V is a volume of the firstshape and A is a surface area of the first shape.
 14. The method ofclaim 10, further comprising: comparing the shape similarity metric forthe first shape and the second shape to another shape similarity metricof a different pair of shapes.
 15. A method of comparing shapes of bodytissues in images of patients, the method comprising: receiving firstdata that defines a first boundary of a first shape of a first bodytissue of a first patient; for each of a plurality of second patients:receiving second data that defines a second boundary of a second shapeof a second body tissue of one of the plurality of second patients;determining, by a computer system, an intersection shape of the firstshape and the second shape; determining, by the computer system, a unionshape of the first shape and the second shape; calculating, by thecomputer system, a difference between the union shape and theintersection shape; and computing, by the computer system, a shapesimilarity metric based on the difference; and identifying a first shapesimilarity metric that satisfies one or more criteria, the first shapesimilarity metric corresponding to a particular second patient.
 16. Themethod of claim 15, wherein the first body tissue is a tumor, whereintreatment information for the particular second patient is retrieved,and wherein the treatment information includes one or more of: ageometry of a radiation beam, a dosage of the radiation beam, and anumber of sessions for treatment using the radiation beam.
 17. Themethod of claim 15, further comprising: aligning the first shape and thesecond shape in a coordinate space.
 18. The method of claim 15, whereinthe one or more criteria specifies a highest shape similarity metric isto be selected.
 19. The method of claim 15, wherein identifying thefirst shape similarity metric that satisfies the one or more criteriaincludes: identifying a set of the shape similarity metrics of theplurality of second patients that satisfy the one or more criteria; andselecting the first shape similarity metric from the set of the shapesimilarity metrics.
 20. The method of claim 19, wherein the one or morecriteria include a threshold value for the shape similarity metrics. 21.The method of claim 19, wherein selecting the first shape similaritymetric from the set of the shape similarity metrics includes:identifying the particular second patient corresponding to the firstshape similarity metric based on treatment outcomes for the secondpatients whose shape similarity metrics satisfy the one or morecriteria.
 22. The method of claim 16, further comprising: determining atreatment plan for the first patient based on the treatment information.23. The method of claim 22, further comprising: performing the treatmentplan using a radiation beam.
 24. The method of claim 15, wherein thefirst shape and the second shapes are determined using a sameshape-determining process.
 25. A computer product comprising anon-transitory computer readable medium storing a plurality ofinstructions that when executed control a computer system to determinean accuracy of shape-determining processes for identifying shapes of abody tissue in one or more images of a patient, the instructionscomprising: receiving first data that defines a first boundary of afirst shape of the body tissue, the first shape being determined by afirst shape-determining process; receiving second data that defines asecond boundary of a second shape of the body tissue, the second shapebeing determined by a second shape-determining process; determining anintersection shape of the first shape and the second shape; determininga union shape of the first shape and the second shape; calculating adifference between the union shape and the intersection shape; computinga shape similarity metric based on the difference; and providing theshape similarity metric for determining an accuracy of the secondshape-determining process relative to the first shape-determiningprocess.